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Mechanisms of ionic mobility and the nature of interactions between mobile and stationary ions in superionic compounds have long been debated. A central issue regards the role of phonons in the superionic state where portions of the lattice exhibit liquid-like behavior. Here, we present results of scattering studies on a superionic conductor which also exhibits low lattice thermal conductivity and potential for application in thermoelectrics. We establish co-existence of acoustic phonons and superionic diffusion, and breakdown of the optical modes in the diffuser sublattice. Further, large anharmonic vibrations of the diffuser sublattice precede the superionic transition, and timescales for diffusion of the mobile species in the superionic state are long compared to the relevant acoustic phonon period. These results demonstrate that anharmonic phonon dynamics is common to the origin of low thermal conductivity and superionicity in this class of materials.